Nuclear spin vector operators

The total angular momentum opJt of each molecule is the sum of the rotational and the two nuclear spin vector operators. The coupling between these is sufficiently weak that one can safely make use of the individual quantum numbers of the two. Details of the situation have been discussed by Bloom.44... 

Here Q represents a vector of normal nuclear coordinates Qu Q2>- , Tn is the nuclear kinetic energy operator, and HSF(Q) is the electronic spin-free Hamiltonian... 

Pauli spin vector Dirac spin vector electron spin magnetic moment nuclear spin magnetic moment rotational magnetic moment electric dipole moment Ioldy Wouthuysen operator gradient operator Laplacian... 

The vectors and denote the Dirac 4x4 matrices for electron i (in standard representation) and the nuclear spin operator for nucleus a. The constants and Kg are nuclear parameters, while is the nuclear spin quantum number. 

The (Tv operator corresponds to a reflection through the molecule-fixed xz plane. If it operates on the spatial and spin coordinates of all electrons, the nuclear displacement vectors, and the rotational wavefunction (expressed in terms of Euler angles, which specify the orientation of the molecule-fixed coordinate system relative to a laboratory-fixed coordinate system), then the eigenvalues of av label the total parity, , of a rotating molecule basis function,... 

The density operator pit) has been formulated for the entire quantum-mechanical system. For magnetic resonance applications, it is usually sufficient to calculate expectation values of a restricted set of operators which act exclusively on nuclear variables. The remaining degrees of freedom are referred to as lattice . The reduced spin density operator is defined by ait) = Tri p(f), where Tri denotes a partial trace over the lattice variables. The reduced density operator can be represented as a vector in a Liouville space of dimension... 

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